A point charge is placed at each corner of a square with side length $a$. The charges all have the same magnitude $q$. Two of the charges are positive and two are negative, as shown in the following figure.

What is the magnitude of the net electric field at the center of the square due to the four charges in terms of $q$ and $a$?

I'm trying to understand this question by using the solution my instructor gave me, but I'm confused.

I found $r=\frac{a}{\sqrt{2}}$, which makes sense. However then it says:

The magnitude of the electric field due to each charge is the same and equal to

 

$$E_q = \frac{kq}{r^2} = \frac{2kq}{a^2}$$

How did they come up with this? I only know the equations $F = \frac{k\lvert q_1q_2\rvert}{r^2}$ and $E = \frac{F_0}{q_0}$ and I can't seem to work out how they got to this point.

A point charge is placed at each corner of a square with side length $a$. The charges all have the same magnitude $q$. Two of the charges are positive and two are negative, as shown in the following figure.

What is the magnitude of the net electric field at the center of the square due to the four charges in terms of $q$ and $a$?

I'm trying to understand this question by using the solution my instructor gave me, but I'm confused.

I found $r=\frac{a}{\sqrt{2}}$, which makes sense. However then it says:

The magnitude of the electric field due to each charge is the same and equal to

$$E_q = \frac{kq}{r^2} = \frac{2kq}{a^2}$$

How did they come up with this? I only know the equations $F = \frac{k\lvert q_1q_2\rvert}{r^2}$ and $E = \frac{F_0}{q_0}$ and I can't seem to work out how they got to this point.

A point charge is placed at each corner of a square with side length $a$. The charges all have the same magnitude $q$. Two of the charges are positive and two are negative, as shown in the following figure.

What is the magnitude of the net electric field at the center of the square due to the four charges in terms of $q$ and $a$?

I'm trying to understand this question by using the solution my instructor gave me, but I'm confused.

I found $r=a/\sqrt{2}$, which makes sense. However then it says:

The magnitude of the electric field due to each charge is the same and equal to $E_q = kq/r^2 = 2kq/a^2$

How did they come up with this? I only know the equations $F = k*|q1q2|/r^2$ and $E = F_0/q_o$ and I can't seem to work out how they got to this point.

A point charge is placed at each corner of a square with side length $a$. The charges all have the same magnitude $q$. Two of the charges are positive and two are negative, as shown in the following figure.

What is the magnitude of the net electric field at the center of the square due to the four charges in terms of $q$ and $a$?

I'm trying to understand this question by using the solution my instructor gave me, but I'm confused.

I found $r=\frac{a}{\sqrt{2}}$, which makes sense. However then it says:

The magnitude of the electric field due to each charge is the same and equal to

$$E_q = \frac{kq}{r^2} = \frac{2kq}{a^2}$$

How did they come up with this? I only know the equations $F = \frac{k\lvert q_1q_2\rvert}{r^2}$ and $E = \frac{F_0}{q_0}$ and I can't seem to work out how they got to this point.

A point charge is placed at each corner of a square with side length $a$. The charges all have the same magnitude $q$. Two of the charges are positive and two are negative, as shown in the following figure.

What is the magnitude of the net electric field at the center of the square due to the four charges in terms of $q$ and $a$?

I'm trying to understand this question by using the solution my instructor gave me, but I'm confused.

I found $r=a/2$, which makes sense. However then it says:

The magnitude of the electric field due to each charge is the same and equal to $E_q = kq/r^2 = 2kq/a^2$

How did they come up with this? I only know the equations $F = k*|q1q2|/r^2$ and $E = F_0/q_o$ and I can't seem to work out how they got to this point.

A point charge is placed at each corner of a square with side length $a$. The charges all have the same magnitude $q$. Two of the charges are positive and two are negative, as shown in the following figure.

What is the magnitude of the net electric field at the center of the square due to the four charges in terms of $q$ and $a$?

I'm trying to understand this question by using the solution my instructor gave me, but I'm confused.

I found $r=a/\sqrt{2}$, which makes sense. However then it says:

The magnitude of the electric field due to each charge is the same and equal to $E_q = kq/r^2 = 2kq/a^2$

How did they come up with this? I only know the equations $F = k*|q1q2|/r^2$ and $E = F_0/q_o$ and I can't seem to work out how they got to this point.